import torch
from torch import nn
from d2l import torch as d2l

n_train = 50
# 长度为50的随机元素排序
x_train, _ = torch.sort(torch.rand(n_train)*5)
print(x_train)# 排序后的状态
print(_)# 这个位置元素原来的index

def f(x):
    return 2 * torch.sin(x) + x**0.8

# torch.normal设置均值为0，标准差为0.5的随机噪声，形状和前面x_train相同
y_train = f(x_train) + torch.normal(0.0, 0.5, (n_train,)) # 训练样本的输出
# 从0开始，每步0.1，一直到5结束
x_test = torch.arange(0, 5, 0.1) # 测试样本
n_test = len(x_test)
print(x_test.shape)
y_truth = f(x_test) # 测试样本真实输出

def plot_kernel_reg(y_hat):
    d2l.plot(x_test, [y_truth, y_hat], 'x', 'y', legend=['Truth', 'Pred'], xlim=[0, 5], ylim=[-1, 5])
    d2l.plt.plot(x_train, y_train, 'o', alpha=0.5)

y_hat = torch.repeat_interleave(y_train.mean(), n_test)
plot_kernel_reg(y_hat)

# 非参数注意力汇聚
X_repeat = x_test.repeat_interleave(n_train).reshape(-1, n_train)
attention_weights = nn.functional.softmax(-(X_repeat - x_train)**2 / 2, dim=1)
y_hat = torch.matmul(attention_weights, y_train)
plot_kernel_reg(y_hat)

d2l.show_heatmaps(attention_weights.unsqueeze(0).unsqueeze(0),
                  xlabel='Sorted training inputs',
                  ylabel='Sorted testing inputs')

# 带参数注意力汇聚
X = torch.ones((2, 1, 4))
Y = torch.ones((2, 4, 6))
print(torch.bmm(X, Y).shape)

weights = torch.ones((2, 10)) * 0.1
values = torch.arange(20.0).reshape((2, 10))
print(f'weights = {weights}')
print(f'values = {values}')
print(f'weights  shape = {weights.shape}')
print(f'weights.unsqueeze(1) shape ={weights.unsqueeze(1).shape}')
print(f'values.unsqueeze(-1).shape = {values.unsqueeze(-1).shape}')
print(torch.bmm(weights.unsqueeze(1), values.unsqueeze(-1)))

# 定义模型
class NWKernelRegression(nn.Module):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        self.w = nn.Parameter(torch.rand(1,), requires_grad=True)

    def forward(self, queries, keys, values):
        # queries和attention_weights的形状为（查询个数，“键-值”对个数）
        queries = queries.repeat_interleave(keys.shape[1]).reshape((-1, keys.shape[1]))
        self.attention_weights = nn.functional.softmax(
            -((queries - keys) * self.w)**2 / 2, dim=1)
        # values的形状为（查询个数， “键-值”对个数）
        return torch.bmm(self.attention_weights.unsqueeze(1),
                         values.unsqueeze(-1)).reshape(-1)

X_tile = x_train.repeat((n_train, 1))
Y_tile = y_train.repeat((n_train, 1))
keys = X_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train, -1))
values = Y_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train, -1))

net = NWKernelRegression()
loss = nn.MSELoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=0.5)
animator = d2l.Animator()

for epoch in range(5):
    trainer.zero_grad()
    l = loss(net(x_train, keys, values), y_train)
    l.sum().backward()
    trainer.step()
    print(f'epoch {epoch + 1}, loss {float(l.sum()):.6f}')
    animator.add(epoch + 1, float(l.sum()))

keys = x_train.repeat((n_test, 1))
values = y_train.repeat((n_test, 1))
y_hat = net(x_test, keys, values).unsqueeze(1).detach()
plot_kernel_reg(y_hat)

d2l.show_heatmaps(net.attention_weights.unsqueeze(0).unsqueeze(0),
                  xlabel = 'Sorted training inputs',
                  ylabel= 'Sorted testing inputs')






